Editing Sampling distribution (section)

==Examples==
[[File:Sampling distribution.png|thumb|Sampling distribution of the sample mean of normally distributed random numbers. With increasing sample size, the sampling distribution becomes more and more centralized.]]
{| class="wikitable"
|-
! Population || Statistic || Sampling distribution
|-
| [[Normal distribution|Normal]]: <math>\mathcal{N}(\mu, \sigma^2)</math> 
| Sample mean <math>\bar X</math> from samples of size ''n''
| <math>\bar X \sim \mathcal{N}\Big(\mu,\, \frac{\sigma^2}{n} \Big)</math>. 
<small>If the standard deviation <math>\sigma</math> is not known, one can consider <math>T = \left(\bar{X} - \mu\right) \frac{\sqrt{n}}{S} </math>, which follows the [[Student's t-distribution]] with <math>\nu = n - 1</math> degrees of freedom. Here <math>S^2</math> is the sample variance, and <math>T</math> is a [[pivotal quantity]], whose distribution does not depend on <math>\sigma</math>. </small>
|-
| [[Bernoulli distribution|Bernoulli]]: <math>\operatorname{Bernoulli}(p)</math>
| Sample proportion of "successful trials" <math>\bar X</math>
| [[Binomial distribution|<math>n \bar X \sim \operatorname{Binomial}(n, p)</math>]]
|-
| Two independent normal populations:<br />
<math>\mathcal{N}(\mu_1, \sigma_1^2)</math> &nbsp;and&nbsp; <math>\mathcal{N}(\mu_2, \sigma_2^2)</math>
| Difference between sample means, <math>\bar X_1 - \bar X_2</math>
| <math>\bar X_1 - \bar X_2 \sim \mathcal{N}\! \left(\mu_1 - \mu_2,\, \frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} \right)</math>
|-
| Any absolutely continuous distribution ''F'' with density ''f''
| [[Median]] <math>X_{(k)}</math> from a sample of size ''n'' = 2''k'' − 1, where sample is ordered <math>X_{(1)}</math> to <math>X_{(n)}</math>
| <math>f_{X_{(k)}}(x) = \frac{(2k-1)!}{(k-1)!^2}f(x)\Big(F(x)(1-F(x))\Big)^{k-1}</math>
|-
| Any distribution with distribution function ''F'' 
| [[Maximum]] <math>M=\max\ X_k</math> from a random sample of size ''n''
| <math>F_M(x) = P(M\le x) = \prod P(X_k\le x)= \left(F(x)\right)^n</math>
|}